Asymptotics of Markov Kernels and the Tail Chain
CORNELL UNIV ITHACA NY
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An asymptotic model for extreme behavior of certain Markov chains is the tail chain. Generally taking the form of a multiplicative random walk, it is useful in deriving extremal characteristics such as point process limits. We place this model in a more general context, formulated in terms of extreme value theory for transition kernels, and extend it by formalizing the distinction between extreme and non-extreme states. We make the link between the update function and transition kernel forms considered in previous work, and we show that the tail chain model leads to a multivariate regular variation property of the finite-dimensional distributions under assumptions on the marginal tails alone.
- Statistics and Probability
- Machinery and Tools